I expected the orbit of the negative-mass planet to look different, somehow. It's strange and non-intuitive that it would be have just like regular mass with regard to the star it's orbiting, but differently with regard to another object in orbit.
Certainly I would have expected the orbit to go higher the faster the planets moved? Is that not the usual effect of increasing speed?
I wonder if it’s using some derived equation for the motion of the planets (re: their orbit) that assumes positive mass, so that part of the simulation understands negative mass but part does not?
> Certainly I would have expected the orbit to go higher the faster the planets moved? Is that not the usual effect of increasing speed?
That rather depends on what you mean. The usual effect of increasing speed in a circular orbit at any given moment is to change it to an elliptical orbit, where the apoapsis is further away from the center of gravity and the object in question moves slower. And if you increase speed again at the apoapsis, you can make the orbit circular again, but the object will be moving much slower than it was to start. Thus two accelerations, both prograde, have the net effect of substantially reducing the prograde speed.
For any given circular orbit, though, lower means faster.
Exactly. Given the previous examples, i would expect the negative mass planet to curve outward on a hyperbolic trajectory due to the repulsive force generated by the suns's gravity
I think the theory for the normal orbit is that the force given by Newtonian gravitation points outward rather than inward, but then the effect of an outward-pointing force on an object of negative mass is to cause an inward-pointing acceleration.
As other people have pointed out, that's inconsistent with other aspects of the simulation, and maybe just means that the author happened to use two equations involving mass in the simulation and the two negative signs cancelled each other out. Whereas using an odd number of equations involving mass would cause a physically noticeable different result.
I actually wonder if one could derive an explicit contradiction in Newtonian dynamics by allowing negative masses. That is, show that there is no trajectory that actually satisfies all of the equations in this case. (But that might also depend on which equations we think are fundamental. E.g., if we break conservation of energy, is that just an interesting consequence that that law doesn't apply anymore, or is that a contradiction?)
